Two students are pushing identical crates across a frictionless floor. the crates are initially at rest. bing applies a horizontal force of 23 n to his crate. bob, who is shorter than bing, pushes on his crate at an angle of 33° below the horizontal, also with a force of 23 n. find the ratio of the masses of the two crates if bing’s crate is moving at twice the speed of bob’s crate after they have traveled a distance of 33.5 m across the floor? (20 pts)

Explanation:

As we know that both the crates are moving at different speed after moving 33.5 m

speed of bling crate = 2 (speed of bob crate)

now we know that

Bling apply force horizontal so the acceleration of his crate is given as

now force of Bob is at 33 degree with the horizontal

so the acceleration of crate of Bob is given as

now we know that work done by Bling and bob on their crate is equal to the kinetic energy of the crate

so for Bling's and Bob'scrate we can say

now the ratio of the work done of two is given as

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

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